System identification device, system identification method, and program

Abstract

To provide a system identification method capable of accurately identifying an object even when training data includes noise.SOLUTION: A system identification device comprises: means for acquiring time-series data of input values to an identification target and observation values indicative of the state of the identification target; means for learning the time-series data to construct a first model which has identified the identification target; means for removing noise from the time-series data on the basis of the time-series data and predicted values of the identification target's state predicted by the first model on the basis of the time-series data; and means for learning the noise-reduced time-series data to construct a second model which has identified the identification target.SELECTED DRAWING: Figure 12

Description

Technical Field

[0001] The present disclosure relates to a system identification device, a system identification method, and a program.

Background Art

[0002] Patent Document 1 discloses a system that estimates a user's drowsiness from observed values such as the user's pulse and respiration while sitting on an automobile or a desk, using a trained model constructed by an Echo State Network (ESN). Similar to a recurrent neural network, ESN is composed of an input layer, a reservoir layer, and an output layer. In the case of ESN, however, after randomly generating the input layer and the reservoir layer, they are not learned, and only the output layer is learned to construct a model. Therefore, the computational cost required for learning is small, and a model can be constructed in a short time. ESN is a type of reservoir computing. When using ESN, for example, it is possible to quickly identify a system during the operation of a machine or the like to be modeled, construct a model, predict the future state of the target using the constructed model, and utilize the prediction for control or the like.

[0003] When using ESN, system identification can be performed with high accuracy in a short time. However, when using observed values from sensors or the like as learning data, the accuracy of the model may decrease due to the influence of noise contained in the observed values.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] One of the objectives is to provide a technology that can build a model with high accuracy even when the learning data contains noise.

Means for Solving the Problem

[0006] According to one aspect of the present disclosure, a system identification device includes means for acquiring time-series data of input values to an object to be identified and observed values indicating the state of the object to be identified; means for constructing a first model that identifies the object to be identified by learning the time-series data; means for removing noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data; and means for constructing a second model that identifies the object to be identified by learning the time-series data from which the noise has been removed.

[0007] According to one aspect of the present disclosure, a system identification method includes acquiring time-series data of input values to an object to be identified and observed values indicating the state of the object to be identified, constructing a first model that identifies the object to be identified by learning the time-series data, removing noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data, and constructing a second model that identifies the object to be identified by learning the time-series data from which the noise has been removed.

[0008] According to one aspect of the present disclosure, a program causes a computer to function as means for acquiring time-series data of input values to an object to be identified and observed values indicating the state of the object to be identified, means for constructing a first model that identifies the object to be identified by learning the time-series data, means for removing noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data, and means for constructing a second model that identifies the object to be identified by learning the time-series data from which the noise has been removed.

Advantages of the Invention

[0009] According to the present disclosure, even when the learning data includes noise, system identification can be performed with high accuracy to construct a target model.

Brief Description of the Drawings

[0010]

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Best Mode for Carrying Out the Invention

[0011] Hereinafter, the system identification apparatus 10 according to each embodiment of the present disclosure will be described with reference to the drawings. In the drawings used in the following description, the configurations of parts not related to the present disclosure may be omitted and not illustrated. In all the drawings, the same or corresponding configurations are denoted by the same reference numerals, and common descriptions may be omitted.

[0012] <First Embodiment> (Configuration of the Apparatus) FIG. 1 is a diagram showing an example of a system identification apparatus according to an embodiment. As shown in FIG. 1, the system identification apparatus 10 includes a data acquisition unit 11, a learning unit 12, a smoothing unit 13, a prediction unit 14, and a storage unit 15. The system identification apparatus 10 learns the observed values measured by a sensor or the like regarding the state and behavior of a machine, system, or the like to be modeled, and constructs a reservoir computing model such as an ESN, thereby performing system identification of the target. Further, the system identification apparatus 10 performs future prediction of the target using the constructed model. The system identification apparatus 10 can be used for the purpose of identifying a non-linear dynamical system in real time and predicting the future state of the non-linear dynamical system. In the following description, an ESN will be described as an example of a reservoir computing model, but it can also be applied to models constructed by other methods. Furthermore, not limited to reservoir computing, it can also be applied to the learning of models constructed by various machine learning, deep learning, and system identification methods.

[0013] The data acquisition unit 11 acquires time-series data of observed values (states) and input values (operation amounts and control values) measured by sensors and the like, and records them in the storage unit 15. The acquired data is used for the learning of the ESN and the future prediction of the target based on the ESN. Here, the target is a non-linear dynamic system such as the dynamics of a moving body such as an AGV (Automatic Guided Vehicle), a forklift, an automobile, an uneven ground transporter, the dynamics of a robot such as the arm operation of a hydraulic excavator or the fork operation of a forklift. When the target is the dynamics of a moving body, the observed value is a value indicating the state of the moving body measured by sensors such as position, attitude, speed, and angular velocity, and the input value is the motor rotation speed, lever operation amount, steering operation amount, operation amount for the accelerator and brake, etc. When the target is the arm operation of a hydraulic excavator, the observed value is a value indicating the state of the arm measured by sensors such as the angles and angular velocities of the bucket, arm, and boom, and the input value is the lever operation amount related to the bucket, arm, and boom, etc. When the target is the fork operation of a forklift, the observed value is a measured value by sensors indicating the state of the fork such as the fork position, lift, tilt, and reach speeds, and the input value is the lever operation amount related to the lift, tilt, and reach, etc.

[0014] The learning unit 12 constructs an ESN using the time-series data of the observed values and input values acquired by the data acquisition unit 11 as learning data. For example, when the object is the dynamics of a moving body, if the observed value (state) at time t and the input value (operation amount) at time t are input to the ESN, learning of the output layer is performed so that the ESN outputs the state of the moving body at time t+1. For example, when the object is the arm operation of a hydraulic excavator, if the observed value (state) at time t and the input value (operation amount) at time t are input to the ESN, learning of the output layer is performed so that the ESN outputs the state of the arm at time t+1. In a general ESN, the measured values measured by the sensor are used for the observed values of the input and output in this learning process. However, in this embodiment, instead of the measured values of the sensor, learning is performed using the values obtained by removing noise and smoothing them by an Extended Kalman Smoother (EKS). This reduces the deterioration of the accuracy of the ESN that occurs when learning only the observed values including noise. For example, the learning unit 12 uses the time-series data of the observed values and input values acquired by the data acquisition unit 11 to create a model for outputting the predicted value of the state of the object to be modeled, which is required in the Kalman smoother. When the observed value and input value at time t are input, an ESN that outputs the observed value at time t+1 is learned. The ESN constructed by this learning is called a "one-stage ESN". The one-stage ESN outputs the time-series data of the predicted values of the state of the object to be modeled based on the time-series data of the observed values and input values acquired by the data acquisition unit 11. The time-series data of the predicted values of the state of the object to be modeled output by the one-stage ESN is processed by the smoothing unit 13 described below to remove noise and become the time-series data of the values indicating the state of the object to be modeled close to the true value (hereinafter referred to as "time-series data close to the true value"). When this time-series data close to the true value is obtained, the learning unit 12 inputs the input value at time t acquired by the data acquisition unit 11 and the value at time t of the time-series data close to the true value, and learns an ESN that outputs the value at time t+1 of the time-series data close to the true value. The ESN constructed by this learning is called a "two-stage ESN".In the control of a moving body or a robot, the values measured by sensors may contain noise, and even if system identification is performed based on the observed values including noise, an accurate model cannot be obtained. Therefore, in the present embodiment, a process of removing noise from the observed values is performed, and system identification is performed using the time-series data after noise removal.

[0015] The smoothing unit 13 smooths the time-series data output by the one-stage ESN constructed by the learning unit 12 using a Kalman smoother. The smoothing unit 13 acquires the time-series data of the observed values and input values acquired by the data acquisition unit 11. On the other hand, it acquires the time-series data of the predicted values of the state of the object to be modeled output by the one-stage ESN constructed by the learning unit 12. Then, the smoothing unit 13 calculates the time-series data of the observed values (the above-mentioned "time-series data close to the true value") obtained by removing the noise included in the sensor measurement values from the observed values of the state by executing a Kalman smoother. Since the Kalman smoother itself is well-known, the detailed description of the processing content is omitted, but the outline of the processing by the smoothing unit 13 is as follows. First, the smoothing unit 13 calculates the estimated value of the state of the object to be modeled at time t obtained by Bayesian estimation from the observed value at a certain time t and the predicted value at time t output by the one-stage ESN by executing a Kalman filter. The smoothing unit 13 performs the same processing for each time to calculate the time-series data of the estimated values of the state. The above is the processing of the Kalman filter included in the Kalman smoother. Subsequently, while referring to the transition of the time-series data of the observed values by the sensor acquired by the data acquisition unit 11, the smoothing unit 13 looks back at the estimated values at each time estimated by the Kalman filter in a way that traces back the time series, determines whether the estimated values are correct, and performs the process of correcting the estimated values at each time. This correcting process is the remaining process of the Kalman smoother. By removing the noise of the observed values by the Kalman smoother and further correcting the estimated values by looking back, the observed values of the time-series state can be made closer to the true value. When estimating the estimated value of the state with the Kalman smoother, state estimation may be performed by another Bayesian filter such as a particle filter instead of the Kalman filter. Also, the smoothing method is not limited to the Kalman smoother, and other methods may be applied. The time-series data close to the true value after performing the Kalman smoother is sent back to the learning unit 12 again and used for the learning of the two-stage ESN.

[0016] The prediction unit 14 performs state prediction of the object to be modeled using the ESN constructed by the learning unit 12. For example, the prediction unit 14 outputs time-series data of state estimation values used in the Kalman smoother based on the time-series data of the observed values and input values acquired by the data acquisition unit 11 and a one-stage ESN. Also, for example, the prediction unit 14 outputs a predicted value indicating the state of the object to be modeled in the future based on the time-series data of the input values acquired by the data acquisition unit 11, the time-series data close to the true value representing the state of the object to be modeled after smoothing, and a two-stage ESN.

[0017] The storage unit 15 stores various data necessary for system identification. For example, the storage unit 15 stores various data acquired by the data acquisition unit 11, a one-stage ESN learned by the learning unit 12, a two-stage ESN, and the like.

[0018] (Overall configuration of the process) FIG. 2 shows a configuration example of a process for constructing a two-stage ESN for the system 1. The input value u(t) at time t is input to the system 1 to be identified. In the system 1, a change occurs in the state due to the input of the input value u(t), and the state becomes y true (t). When this state is detected by the sensor 2, the observed value y(t) is obtained. The system 1 and the system identification device 10 are connected by a network, and a set of the input value u(t) and the observed value y(t) is recorded in the storage unit 15, for example. The input value u(t) is input to the system 1 at every moment, and the sensor 2 measures the state of the system 1 at each time. During the operation of the system 1, this process is repeatedly executed, and time-series data of the input value u(t) and the observed value y(t) is accumulated in the storage unit 15. y(t) is past data with noise.

[0019] Next, the learning unit 12 reads out the time-series data of the input value u(t) and the observed value y(t) with noise from the memory unit 15, and constructs a one-stage ESN 121 using this time-series data as learning data. Next, the smoothing unit 13 uses the input value u(t) and the observed value y(t) with noise, and the one-stage ESN 121 to remove (denoise) the noise from the time-series data of the observed value y(t) by the Kalman smoother 131. The time-series data of the denoised observed value y^(t) (time-series data close to the true value) is recorded in the memory unit 15. Next, the learning unit 12 reads out the time-series data of the denoised y^(t) and the time-series data of the input value u(t) from the memory unit 15, and constructs a two-stage ESN 122 using this time-series data as learning data. When the two-stage ESN 122 is constructed, hereafter, the future state of the system 1 is predicted using the two-stage ESN 122, and the predicted value is used for control of the system 1 and the like.

[0020] (Learning process) With reference to FIG. 3, the flow of the process of constructing an ESN will be described. FIG. 3 is a flowchart showing an example of the system identification process according to the embodiment. Each of the following processes shown in FIG. 3 may be executed online in real time, for example, during the operation of a machine or the like to be modeled. The data acquisition unit 11 acquires learning data (step S1). For example, the data acquisition unit 11 acquires the time-series data of the input value u(t) and the observed value y(t) from a machine or the like to be modeled, and records it in the memory unit 15.

[0021] Next, the learning unit 12 constructs a first-stage ESN 121 (step S2). Based on the time-series data of the input value u(t) and the observed value y(t), the learning unit 12 constructs a first-stage ESN 121 that outputs the observed value y(t + 1) when the input value u(t) and the observed value y(t) are input. The learning unit 12 records the constructed first-stage ESN 121 in the memory unit 15. The first-stage ESN 121 is used in the next Kalman smoother.

[0022] Next, the smoothing unit 13 smooths the observed values (step S3). The smoothing unit 13 performs a Kalman smoother based on the time-series data of the input value u(t) and the observed value y(t), and the time-series data of the observed value ŷ(t) predicted by the first-stage ESN121 from the input value u(t) and the observed value y(t), to smooth the time-series data of the observed value ŷ(t). The smoothing unit 13 records the time-series data of the smoothed observed value ŷ(t) (time-series data close to the true value) in the storage unit 15.

[0023] Next, the learning unit 12 constructs the second-stage ESN122 (step S4). The learning unit 12 constructs a second-stage ESN122 that outputs the smoothed observed value ŷ(t + 1) when the input value u(t) and the smoothed observed value ŷ(t) are input, based on the time-series data of the input value u(t) and the time-series data of the smoothed observed value ŷ(t). The learning unit 12 records the constructed second-stage ESN122 in the storage unit 15.

[0024] (Prediction process) With reference to FIG. 4, the flow of the prediction process by the constructed two-stage ESN will be described. FIG. 4 is a flowchart showing an example of the prediction process according to the embodiment. The following process shown in FIG. 4 may be executed online in real time, for example, during the operation of a machine to be modeled or the like. The data acquisition unit 11 acquires the observed value and the input value at time t (step S11). For example, the data acquisition unit 11 outputs the input value u(t) and the observed value y(t) to the prediction unit 14 from a machine to be modeled or the like. Next, the prediction unit 14 performs prediction using the second-stage ESN 122 (step S12). The prediction unit 14 inputs the input value u(t) and the observed value y(t) into the second-stage ESN 122 to obtain a predicted value ŷ(t + 1) indicating the state of the target at time t + 1. Here, for the observed value y(t) to be input, a process of removing noise included in the sensor may be performed. For example, the smoothing unit 13 may perform real-time noise removal of the observed value y(t) by a Bayesian filter such as a Kalman filter or a particle filter and output the value to the prediction unit 14. In this case, the prediction unit 14 inputs the input value u(t) and the observed value y(t) after noise removal into the second-stage ESN 122 to predict the predicted value ŷ(t + 1) at time t + 1. Also, the second-stage ESN 122 may be constructed online and in real time during the operation of a machine or the like to be modeled. Next, the prediction unit 14 outputs the predicted value ŷ(t + 1) to another device (for example, a control device of a moving body or a robot) (step S13).

[0025] (Evaluation of Prediction Accuracy) Next, with reference to FIGS. 5 to 10, the effects of the present embodiment will be described. In order to evaluate the identification method of the non-linear dynamic system, it is verified how accurately the chaos system can be predicted. Hereinafter, taking the Lorenz system and the Rossler system, which are widely used as benchmarks, as examples, the evaluation results regarding the prediction accuracy of the two-stage ESN are shown.

[0026] (Evaluation by Lorenz System) Figures 5 to 7 show the evaluation results using the Lorenz system. In the evaluation of the prediction accuracy using the Lorenz system, for the chaotic system represented by the following Lorenz equations, with the initial values (x, y, z) = (1, 1, 1), σ = 10, ρ = 28, β = 8 / 3, only the x - coordinate data for 1000 steps was used to train the ESN to predict the value of the x - coordinate at step T + 1 from the value of the x - coordinate at step T. Then, for the 500 steps after the 1000 steps used for training, the constructed ESN was used to predict the values of the x - coordinate of the next step one after another, and an evaluation was made of how accurately the prediction could be made.

[0027] · Lorenz equations dx / dt = σ(y - z) dy / dt = x(ρ - z) - y dz / dt = zy - βz

[0028] Figure 5 shows an example of the prediction results by the ESN constructed by learning the observation data without noise. The vertical axis of Figure 5 represents the value of the x - coordinate, and the horizontal axis represents the number of steps. Graph L1 shows the value of the x - coordinate of the Lorenz system after the 1000 steps used for learning, and graph L2 shows the value of the x - coordinate predicted by the ESN. The 0 on the horizontal axis of Figure 5 indicates the 1000th step of the actual data. As shown in the figure, the ESN can accurately predict up to about 0 to 160 steps.

[0029] Figure 6 shows an example of the prediction results by the ESN constructed with noise in the observation data. The vertical axis of Figure 6 represents the value of the x - coordinate, and the horizontal axis represents the number of steps. Noise following a Gaussian distribution (mean μ = 0, standard deviation σ = 1.5) was added to the learning data of the ESN (the x - coordinate values for 1000 steps). Graph L1 shows the value of the x - coordinate of the Lorenz system after the 1000 steps, and graph L3 shows the value of the x - coordinate predicted by the ESN (corresponding to a one - layer ESN) constructed from the learning data containing noise. Comparing with the example in Figure 5, it can be seen that the prediction accuracy has decreased. Thus, when observation noise exists, the prediction accuracy of the non - linear dynamic system by the ESN decreases.

[0030] Fig. 7 shows an example of the prediction results by a two - stage ESN constructed by training the observation data including noise. The same noise as in the case of Fig. 6 was added to the training data of the two - stage ESN. Graph L1 shows the value of the x - coordinate of the Lorenz system, and graph L4 shows the value of the x - coordinate predicted by the two - stage ESN according to the present embodiment constructed from the training data including noise. As shown in the figure, it can be seen that the prediction accuracy is equal to or higher than that of the example shown in Fig. 5.

[0031] (Evaluation by the Lorenz system) Figs. 8 to 10 show the evaluation results using the Lorenz system. In the evaluation using the Lorenz system, for the chaotic system represented by the following Lorenz equations, with the initial values (x, y, z)=(1, 1, 1), a = 0.5, b = 2, c = 4, the ESN was trained to predict the value of the x - coordinate at step T + 1 from the value of the x - coordinate at step T using only the data of the x - coordinate for 1000 steps. Then, for the 500 steps after the 1000 steps used for training, the constructed ESN was used to predict the value of the x - coordinate of the next step one after another, and an evaluation was made of how accurately the prediction could be made.

[0032] ·Lorenz equations dx / dt=-y - z dy / dt=x + ay dz / dt=b+(x - c)z

[0033] Fig. 8 shows an example of the prediction results by an ESN constructed by training the observation data without noise. The vertical axis of Fig. 8 represents the value of the x - coordinate, and the horizontal axis represents the number of steps. Graph R1 shows the value of the x - coordinate of the Lorenz system after 1000 steps, and graph R2 shows the value of the x - coordinate predicted by the ESN. As shown in the figure, the value of the x - coordinate can be accurately predicted by the ESN until slightly beyond 0 to 100 steps.

[0034] Fig. 9 shows an example of the prediction result by the ESN constructed by training the observation data including noise. The vertical axis in Fig. 9 represents the value of the x coordinate, and the horizontal axis represents the number of steps. Noise following a Gaussian distribution (mean μ = 0, standard deviation σ = 1.5) was added to the learning data (the values of the x coordinate for 1000 steps) of the ESN. Graph R1 shows the value of the x coordinate of the Rössler system, and graph R3 shows the value of the x coordinate predicted by the ESN (corresponding to a one - stage ESN) constructed from the learning data including noise. Compared with the example shown in Fig. 8, the prediction accuracy has decreased. It can be seen that in the case of the Rössler system as well as the Lorenz system, when the ESN is constructed with learning data including noise, the prediction accuracy decreases.

[0035] Fig. 10 shows an example of the prediction result by the two - stage ESN constructed by training the observation data including noise. The same noise as in the case of Fig. 9 was added to the learning data of the ESN. Graph R1 shows the value of the x coordinate of the Rössler system, and graph R4 shows the value of the x coordinate predicted by the two - stage ESN according to the present embodiment constructed from the learning data including noise. As shown in the figure, a prediction result with higher accuracy than the example without noise shown in Fig. 8 is obtained.

[0036] (Effect) As described above, according to the first embodiment, even when the learning data includes noise, the Kalman smoother is used to generate the learning data with noise removed, and by learning the learning data after noise removal, a model with high prediction accuracy can be constructed.

[0037] <Second Embodiment> Next, with reference to Fig. 11, another method for constructing the ESN will be described. In this method, the process of constructing the ESN, denoising the learning data by the Kalman smoother, and then constructing the ESN of the next stage is repeated a plurality of times. Fig. 11 shows a configuration example of the process for constructing an N - stage ESN for system 1. Similar to the process described in Fig. 2, the input value u(t) at time t is input to the system 1 to be identified. Due to the input of the input value u(t), the state of system 1 is ytrue It becomes (t). When this state is detected by sensor 2, the observed value y(t) is obtained. During the operation of system 1, this process is repeatedly executed, and time-series data of the input value u(t) and the observed value y(t) are accumulated in the storage unit 15.

[0038] Next, the learning unit 12 reads out the time-series data of the input value u(t) and the observed value y(t) with noise from the storage unit 15, and constructs a one-stage ESN121 using this time-series data as learning data. Next, the smoothing unit 13 uses the input value u(t) and the observed value y(t), and a Kalman smoother 131 to generate a denoised observed value (time-series data close to the true value), and records it in the storage unit 15. Next, the learning unit 12 reads out the time-series data of the denoised observed value and the time-series data of the input value u(t) from the storage unit 15, and constructs a two-stage ESN122 using this time-series data as learning data. Next, the smoothing unit 13 uses the input value u(t) and the denoised observed value, and a second Kalman smoother 132 to further smooth the denoised observed value, and records it in the storage unit 15. Thereafter, the process of smoothing the learning data using the k-stage (3 ≤ k ≤ n - 1) ESN with the k-th Kalman smoother 13k, and constructing a (k + 1)-stage ESN by learning the smoothed learning data is repeated until k = n - 1 (n is a predetermined natural number). By such a process, the accuracy of the learning data is improved, and by constructing an ESN using the learning data with improved accuracy, the target system can be identified with higher accuracy.

[0039] <Third Embodiment> FIG. 12 is a second diagram showing an example of the system identification device according to the embodiment. The system identification device 800 includes an acquisition means 801 that acquires time-series data of input values to the object to be identified and observed values indicating the state of the object to be identified, a first construction means 802 that learns the time-series data and constructs a first model that identifies the object to be identified, a removal means 803 that removes noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data, and a second construction means 804 that learns the time-series data from which the noise has been removed and constructs a second model that identifies the object to be identified.

[0040] FIG. 13 is a second flowchart showing an example of the system identification process according to the embodiment. The acquisition means 801 acquires time-series data of input values to the object and observed values indicating the state of the object to be identified (step S801). The first construction means 802 learns the time-series data and constructs a first model that system-identifies the object to be identified (step S802). The removal means 803 removes noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data (step S803). The second construction means 804 learns the time-series data from which the noise has been removed and constructs a second model that identifies the object to be identified (step S804).

[0041] FIG. 14 is a diagram showing an example of the hardware configuration of the system identification device according to the embodiment. The computer 900 includes a CPU 901, a main storage device 902, an auxiliary storage device 903, an input / output interface 904, and a communication interface 905. The above-described system identification device 10 is implemented in the computer 900. And each of the above-described functions is stored in the auxiliary storage device 903 in the form of a program. The CPU 901 reads the program from the auxiliary storage device 903, expands it in the main storage device 902, and executes the above processing according to the program. Further, the CPU 901 secures a storage area in the main storage device 902 according to the program. Further, the CPU 901 secures a storage area in the auxiliary storage device 903 for storing data during processing according to the program.

[0042] Note that a program for realizing all or part of the functions of the system identification device 10 may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be read into a computer system and executed to perform processing by each functional unit. Here, the "computer system" shall include hardware such as an OS and peripheral devices. Also, the "computer system" shall include a homepage providing environment (or display environment) if the WWW system is used. Further, the "computer-readable recording medium" refers to a portable medium such as a CD, DVD, USB, etc., and a storage device such as a hard disk built into a computer system. Also, when this program is distributed to the computer 900 via a communication line, the computer 900 that has received the distribution may expand the program in the main storage device 902 and execute the above processing. Also, the above program may be for realizing a part of the functions described above, and may further be a program that can be realized in combination with a program already recorded in the computer system for realizing the functions described above.

[0043] As described above, one embodiment of the present disclosure has been described in detail with reference to the drawings. However, the specific configuration is not limited to the above, and various design changes and the like can be made without departing from the gist of the invention. Also, one aspect of the present disclosure can be variously changed within the scope shown in the claims, and embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present disclosure. Also, configurations in which elements described in the above embodiments and modification examples and elements having the same effects are replaced with each other are included. And each embodiment can be combined with other embodiments as appropriate.

[0044] Some or all of the above embodiments may be described as follows, but are not limited thereto.

[0045] (Supplementary Note 1) Means for acquiring time-series data of input values to the object to be identified and observed values indicating the state of the object to be identified, means for constructing a first model that identifies the object to be identified by learning the time-series data, based on the time-series data and a predicted value of the state of the object to be identified predicted by the first model based on the time-series data, means for removing noise from the time-series data, and means for constructing a second model that identifies the object to be identified by learning the time-series data from which the noise has been removed. A system identification device comprising:

[0046] (Appendix 2) The means for constructing the first model constructs the first model, and the means for removing noise removes noise from the time-series data using the first model. After that, the means for constructing the first model learns the time-series data from which the noise has been removed and reconstructs the first model again. The means for removing noise removes noise from the time-series data using the first model reconstructed again. This process is repeated one or more times. The means for constructing the second model learns the time-series data from which the noise has been removed and generated by repeating this process one or more times, and constructs the second model. The system identification device according to Appendix (1).

[0047] (Appendix 3) The object to be identified is a non-linear dynamic system whose behavior changes non-linearly over time. The system identification device according to Appendix (1) or Appendix (2).

[0048] (Appendix 4) The first model and the second model are reservoir computing. The system identification device according to any one of Appendices (1) to (3).

[0049] (Appendix 5) The first model and the second model are echo state networks. The system identification device according to any one of Appendices (1) to (3).

[0050] (Appendix 6) The means for removing the noise is the system identification device according to any one of Appendices (1) to (5), which removes the noise by a Kalman smoother.

[0051] (Appendix 7) The means for removing the noise is the system identification device according to any one of Appendices (1) to (6), which calculates time-series data of an estimated value indicating the state of the object to be identified by a Bayesian filter based on the time-series data of the observed values and the time-series data of the predicted values predicted by the first model based on the time-series data of the observed values, and further corrects the time-series data of the estimated value.

[0052] (Appendix 8) The means for acquiring the time-series data acquires the time-series data from the object to be identified during the operation of the object to be identified, the means for constructing the first model constructs the first model during the operation of the object to be identified, the means for removing the noise removes the noise during the operation of the object to be identified, and the means for constructing the second model constructs the second model during the operation of the object to be identified. It is the system identification device according to any one of Appendices (1) to (7).

[0053] (Appendix 9) The system identification device according to any one of Appendices (1) to (8), further comprising means for predicting the state of the object to be identified by inputting the input value and the observed value into the second model.

[0054] (Appendix 10) The means for acquiring the time-series data acquires the time-series data from the object to be identified during the operation of the object to be identified. The means for constructing the first model constructs the first model during the operation of the object to be identified. The means for removing the noise removes the noise during the operation of the object to be identified. The means for constructing the second model constructs the second model during the operation of the object to be identified. The means for predicting predicts the future state of the object to be identified during operation based on the second model constructed during the operation of the object to be identified, and is the system identification device according to Supplementary Note (9).

[0055] (Supplementary Note 11) A system identification method for acquiring time-series data of input values to the object to be identified and observed values indicating the state of the object to be identified, constructing a first model for identifying the object to be identified by learning the time-series data, and removing noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data, and constructing a second model for identifying the object to be identified by learning the time-series data from which the noise has been removed.

[0056] (Supplementary Note 12) The method for system identification according to Supplementary Note (9), wherein the process of constructing the first model, removing noise from the time-series data using the first model, then learning the time-series data from which the noise has been removed to reconstruct the first model, and removing noise from the time-series data using the first model reconstructed again is repeated once or a plurality of times, and then the time-series data from which the noise has been removed generated by repeating the process once or a plurality of times is learned to construct the second model.

[0057] (Supplementary Note 13) A program for causing a computer to function as means for acquiring time-series data of input values to an object to be identified and observed values indicating the state of the object to be identified, means for constructing a first model that identifies the object to be identified by learning the time-series data, means for removing noise from the time-series data based on the time-series data and predicted values of the state of the object to be identified predicted by the first model based on the time-series data, and means for constructing a second model that identifies the object to be identified by learning the time-series data from which the noise has been removed.

[0058] (Appendix 14) The means for constructing the first model constructs the first model, the means for removing noise removes noise from the time-series data using the first model, then the means for constructing the first model learns the time-series data from which the noise has been removed and reconstructs the first model again, and the means for removing noise removes noise from the time-series data using the first model reconstructed again. This process is repeated one or more times. The means for constructing the second model learns the time-series data from which the noise has been removed and generated by repeating this process one or more times, and constructs the second model. The program according to Appendix (11).

[0059] Regarding the system identification methods in Appendices 11 to 12 and the programs in Appendices 13 to 14, the aspects in Appendices 3 to 10 can be applied.

Explanation of Reference Numerals

[0060] 10 ··· System identification device 11 ··· Data acquisition unit 12 ··· Learning unit 13 ··· Smoothing unit 14 ··· Prediction unit 15 ··· Storage unit 800 ··· System identification device 801 ··· Acquisition means 802 ··· First construction means 803 ··· Removal means 804 ··· Second construction means 900 ··· Computer 901 ··· CPU 902 ··· Main memory device 903 ··· Auxiliary storage device 904 ··· Input / output interface 905 ··· Communication interface

Claims

1. Means for acquiring time series data of input values to the object to be identified and observed values indicating the state of the object to be identified; Means for constructing a first model that identifies the object to be identified by learning the time series data; Means for removing noise from the time series data based on the time series data and predicted values of the state of the object to be identified predicted by the first model based on the time series data; Means for constructing a second model that identifies the object to be identified by learning the time series data from which the noise has been removed; A system identification device comprising:

2. The means for constructing the first model constructs the first model, The means for removing the noise removes the noise from the time series data using the first model, and then, The means for constructing the first model learns the time series data from which the noise has been removed to reconstruct the first model again, and the means for removing the noise removes the noise from the time series data using the reconstructed first model, and this process is repeated one or more times, The means for constructing the second model learns the time series data from which the noise has been removed, which is generated by repeating the above process one or more times, to construct the second model. The system identification device according to Claim 1.

3. The object to be identified is a non-linear dynamic system whose behavior changes non-linearly over time. The system identification device according to Claim 1 or Claim 2.

4. The first model and the second model are reservoir computing. The system identification device according to Claim 1 or Claim 2.

5. The first model and the second model are echo state networks. The system identification device according to Claim 1 or Claim 2.

6. The means for removing the noise removes the noise by a Kalman smoother. The system identification device according to Claim 1 or Claim 2.

7. Means for predicting the state of the object to be identified by inputting the input value and the observed value into the second model. The system identification device according to Claim 1 or Claim 2, further comprising:

8. The means for acquiring the time series data acquires the time series data from the object to be identified during the operation of the object to be identified, The means for constructing the first model constructs the first model during the operation of the object to be identified. The means for removing the noise removes the noise during the operation of the object to be identified, The means for constructing the second model constructs the second model during the operation of the object to be identified, The means for predicting predicts the future state of the object to be identified during operation based on the second model constructed during the operation of the object to be identified. The system identification device according to claim 7.

9. Obtain time-series data of input values to the object to be identified and observed values indicating the state of the object to be identified, By learning the time-series data, construct a first model that identifies the object to be identified, Based on the time-series data and the predicted values of the state of the object to be identified predicted by the first model based on the time-series data, remove noise from the time-series data, By learning the time-series data from which the noise has been removed, construct a second model that identifies the object to be identified. System identification method.

10. A computer, Means for obtaining time-series data of input values to the object to be identified and observed values indicating the state of the object to be identified, Means for constructing a first model that identifies the object to be identified by learning the time-series data, Means for removing noise from the time-series data based on the time-series data and the predicted values of the state of the object to be identified predicted by the first model based on the time-series data, Means for constructing a second model that identifies the object to be identified by learning the time-series data from which the noise has been removed, A program for causing it to function as such.

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